Spatio-temporal Bayesian regression for room impulse response reconstruction with spherical waves

The reconstruction of sound fields in a room from a limited set of measurements is a central problem in acoustics, with relevant applications in e.g. acoustic analysis, audio, or sound field control. Conventional approaches rely on measuring the room impulse response (RIR) at several locations in the room, and fitting a wave model that enables to estimate the field at other locations – via solving an inverse problem. Previous studies have shown that the reconstruction of RIRs strongly depends on the physical model and the regularization method used to solve the problem, and that enforcing sparsity is beneficial for the reconstruction of the early part of the RIR. This work studies Bayesian regression with time-dependent regularization in order to exploit the temporal properties of RIRs for a better reconstruction. The inverse problem is solved in the time domain, where hierarchical Bayes is applied in order to explicitly promote solutions where the density of waves in the sound field increases as a function of time. The performance of the proposed model is studied with experimental measurements, and compared to classical Bayesian reconstruction methods.